Importing a existing model
I think this is what you're asking for, it deletes all the groups whose name appears in the first column of your list. I'm not sure why you decided to go with two columns.
import bpy
C = bpy.context

import bpy


name_list = [
    # old name - new name
['Camo','Camo'],
['Corr','Corr'],
['Eyes','Eyes'],
['Head','head'],
['head_injury','head_injury'],
['Jaw_LM','Jaw_LM'],
['Jaw_RM','Jaw_RM'],
['Lip_LC','Lip_LC'],
['Lip_LwLF','Lip_LwLF'],
['Lip_LwRF','Lip_LwRF'],
['Lip_RC','Lip_RC'],
['Nose_L','Nose_L'],
['Nose_R','Nose_R'],
['Zig_LT','Zig_LT'],
['Zig_RT','Zig_RT'],
]

ob =  C.active_object

for n in name_list:
    if n[0] in ob.vertex_groups:
        grp=ob.vertex_groups[n[0]]
        print(grp.name)
        ob.vertex_groups.remove(grp)